Self-congruent point in critical matrix product states: An effective field theory for finite-entanglement scaling
Year: 2025
Type: article
Abstract: We set up an effective field theory formulation for the renormalization flow of matrix product states (MPS) with finite bond dimension, focusing on systems exhibiting finite-entanglement scaling close to a conformally invariant critical fixed point. We show that the finite MPS bond dimension \chi χ is equivalent to introducing a perturbation by a relevant operator to the fixed-point Hamiltonian. The fingerprint of this mechanism is encoded in the \chi χ -independent universal transfer matrix’s gap ratios, which are distinct from those predicted by the unperturbed Conformal Field Theory (CFT). This phenomenon defines a renormalization group self-congruent point, where the relevant coupling constant ceases to flow due to a balance of two effects; When increasing \chi χ , the infrared scale, set by the correlation length \xi(\chi) ξ ( χ ) , increases, while the strength of the perturbation at the lattice scale decreases. The presence of a self-congruent point does not alter the validity of the finite-entanglement scaling hypothesis, since the self-congruent point is located at a finite distance from the critical fixed point, well inside the scaling regime of the CFT. We corroborate this framework with numerical evidence from the exact solution of the Ising model and density matrix renormalization group (DMRG) simulations of an effective lattice model.
Source: SciPost Physics
Authors: Jan Thorben Schneider, Atsushi Ueda, Yifan Liu, Andreas Martin Läuchli, Masaki Oshikawa, Luca Tagliacozzo
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
Funders: Watanabe Foundation, Georgia Space Grant Consortium, Comunidad de Madrid, European Commission, École Polytechnique Fédérale de Lausanne, Fonds Wetenschappelijk Onderzoek, University of Tokyo, Japan Society for the Promotion of Science, Consejo Superior de Investigaciones Científicas, Agencia Estatal de Investigación, NextGenerationEU
Awards: G1175115578, G1198809255, G129255482, G1423675079, G210041235, G2262748287, G2601397997, Elucidation of thermalization as a nonlinear response, G300979063, G34346518, G3480869486, G3681454997, G4042783231, G425668148, G4442677895, G4511186732, G4526231891, G4534730369, G480488906, G5080475149, G5195188938, G524312865, G5338730000, G7054776850, G7084143925, G7434936867, 古代説話における諸寺縁起の研究, G7653757565
OpenAlex ID: W4404370630